An investigation of some free energies of absorption.

S-S • chool

California

Mom

t~tz

A^ - AbSoRPT»oO

AW INVESTIGATION OF SOME FREE ENERGIES OF
ADSORPTION

by
Sigmund Abraham, Jr.

A THESIS

Presented to the Graduate Faculty of Lehigh University

in Candidacy for the Degree of Master of Science

Lehigh University
1956

Thesis

This thesis is presented to the Faculty of Lehigh Univer-
sity in partial fulfillment of the requirements for the decree
of Master of Science in Chemistry.

This thesis is accepted and approved in partial fulfillment
of the requirements for the decree of Master of Science.

CONTENTS

Introduction 1

Heats of Wetting 2

Free Energy of Adsorption 8

Nature of Physical Adsorption 11

Literature Data 16

Results and Conclusions 18

Appendix 25

References 29

Biography 30

- iii -

INTRODUCTION

The wetting of solids is a phenomenon of threat natural and
industrial importance. The spreading of a lubricant over a surface
to be lubricated and the spreading and adhesion of paints and pro-
tective coatings are all dependent upon this phenomenon. Other
illustrations include waterproofing of fabrics, printing, and the
process of washing with soaps .

In this paper an inquiry is made to determine the correlation
of heats of wetting as measured with a calorimeter and free energy
changes calculated from isotherm data. The interaction of various
liquids with hydrophilic solids is considered from such data as is
available in the chemical literature.

- 1 -

HEATS OF WETTING

When a solid is immersed in a liquid and physical adsorption occurs,
the resulting decrease in surface energy may be measured by a sensitive
calorimeter [l] . Although heats of immersion are actually measured, it
is customary to define heats of emersion and this practice will be fol-
lowed here .

The total surface energy (E_), or enthalpy, (H~), of a clean,
non-pourous solid prior to immersion is given by

where ]T is the area of the solid and ?q is its surface tension or

free surface energy. On immersion in a liquid the solid surface is

replaced by a solid - liquid interface with an enthalpy, (H ), which

is defined as

oy
HSL " rSL I 'SL " T (^r)p ' • <2)

The subscripts refer to the interface. If the areas are equal,
^0 = <<— or > and the enthalpy of emersion, (IL,/- \), is

"■(at) " Hs - Hst - * I *8 - >sl " «ar - -5T>P) (3)

or per unit area

Vst) - ^ - 's - >SL - T (& - Tr>P,£ • «

- 2 -

The change in enthalpy is related to changes in internal ener^
by the equation

Ah = Ae + Apv

or at constant pressure

Ah ■ Ae + pAv

Since Av is small and cannot be detected within the limits of experi-
mental error,

Ah = Ae .

The energy of adhesion, € /„ \ , is the change in internal energy
when a liquid is separated from a solid at their interface to give
clean surfaces of both. The energy of adhesion is given by

£A(SL) - €S " €SL + *L m *£ + \ (5)

where eg , €„. , and c. refer to the internal energies of the
solid, interface and liquid respectively. €_ is the internal energy
of emersion and since h = € it may be seen that the energy of adhesion
is simply equal to the heat of emersion, h-,, plus the surface energy of
the liquid. This latter quantity is obtained from the surface tension
and the temperature variation of the surface tension of the liquid.

If the solid is no longer clean (that is, if a film is adsorbed
on the surface) the free surface energy changes from y„ to some lower
value 7__ and the total surface energy from

3 -

to

o7s

hs = 7s " T (St^p, ^

°75f

hsf = 7sf " T ("^r)P>1

The enthalpy of emersion, hwq fT \ > per unit area of solid containing
adsorbed molecules is given by

MsfL) = hSf " hSL = 7Sf " 7SL " T(~T *"*P,£' (6)

The following processes, (Fig. l), define the heat of desorption,
h / v , and establish the relationship between the heat of desorp-
tion and the heat of emersion:

(A.) A solid is emersed from n mules of liquid into a vacuum.
Here, n, is assumed to be large compared with the n moles considered
in the next step.

<* = VSL) (7)

(B.) The solid is emersed from n moles of liquid into the
vapor of the liquid at the pressure p carrying with it a film of
just the correct thickness to give it equilibrium with the vapor at
this pressure . The amount of liquid removed in this film is n moles .

^ = Van) (8)

(C.) Of the n, moles of liquid left in (A.) evaporate n moles
with heat of evaporation, X , leaving (n, - n) moles, which is the

- h -

Lvalont roccss

_/v

1 era solid
with n uolos
va ior

n' moles of liquid

. 1

- 5 -

amount of liquid left in (B.).

AH = nX (9)

(D.) Subtract equation (3) from the sum of equations (7) and (9),
since this will give the increase in the value of the heat function
when the film of n moles is vaporized from the surface of the solid.
The heat of desorption, ^n^uSf ^ ' then is

VvSf ) = MSL) " VsfL) + nk ' (i0)

By substituting equations (l) and (6) for h^/a T \ an(i h_/ qfT \ in
equation (10) the heat of desorption is found to be

^7S °73f

^(vsf) = 7s " 7sf " T (St St"^ + nx * (11)

The heats of desorption may be expressed in calories per gram,
calories per mole, or as calories per unit area of the surface of the
solid.

From the relation, AH = AF - TAS , the corresponding free
energy terms for a surface and solid-liquid interface are found. The
free energy of emersion, f , is defined as

fe ■ h - ?SL ' (12)

The work of adhesion. WA,„T x , for a solid and a liquid is defined

' A(SL) '

as

WA(SL) " 7S - 7SL + 7L * (13)

- 6 -

The spreading pressure, n , is defined as

*e " 7S 7SL " 7L

- 7 -

(1U)

FREE ENERGY OF ADSORPTION
The Gibbs f function is defined as

f - ESo " T SSo " "l ri - "2 r2 to)

where E_ is the total surface ener^-, S is the surface entropy,
T. is the surface density of species i , and u.. is the chemical
potential of species i [3]. Also,

I = 7Sf " 7So = "* ' (l6)

n , the spreading pressure or change in free energy, is then equal to
the difference between the free surface energy of a clean, solid surface,
ya , and the free surface ener<^y, 7a„ , of the solid when in equilib-

OO ol

rium with a dissimilar fluid component. For a system consisting of one
adsorbent and one adsorbate, the differential, d« , is

d* = sSo dT + r± dux + r2 du2 . (17)

If isothermal conditions are maintained and if the Gibbs plane from
which adsorption is measured is chosen so the surface density of adsor-
bent, r, , is zero,

d* = r2 du2 (18)

or

r* " «2W • (19)

If the fluid contig b > the sjlid surface is a gas ur /a^r, the
chemical potential and fugacity, f , are related by the equation

du2 = RT d(ln f2) , (20)

where R is the usual gas constant. At low pressures, the relation

RT d(ln f ) = RT d(ln p0)
is valid, and substituting, dn is found to be

d« = rt r2 d(ln p2) , (21)

where p is the equilibrium pressure of the adsorbed vapor measured
from zero to its saturation pressure, p ? . Integration results in

P2

r dM = 7So - ?SV = RT f F2 d(in P2) ' (22)
Jo Jo

where y0.t is the free surface energy of the solid in equilibrium

with the vapor .

The quantity yc - ya. is the two dimensional spreading pressure
oO fcsV

of the adsorbed film on the solid surface, or, the free energy of
emersion at constant temperature of a unit surface of clean solid in
an infinite amount of vapor at pressure p . If the solid is
immersed in a saturated vapor of pressure p ? , equation (22) becomes

/

rPo2

d» = >So " 'sVe " RT/ r2 d(ln p2> ' (23)

o o

where * is the spreading pressure at saturation, or the corresponding
decrease in free surface energy, and y is the free surface energy

- 9 -

of the solid in equilibrium with the saturated vapor.
The surface density, T , is defined as

£V

2_

v

(2U)

where v~ is the measured adsorption, £ is the specific area of the

solid, V is the molar volume of the vapor, and t is the thickness

RT
of the surface region. Assuming perfect gas behavior, V = — ,

Vo

and substituting,

2

2 £V RT

Equation (23) then becomes

(25)

r p

RT

o2

v d(ln p2)

^ o

r p

o2

f T d^;

(26)

The second term makes no significant contribution and may be neglected.

The expression for free energy is then

RT

/

Jo2

v d(ln p2)

(27)

For decreases in free energy at pressures less than saturation the
equation is given as

* = H J V d(ln P2>

(28)

The evaluation of the equation requires the simultaneous deter-
mination of the volume of material adsorbed and the equilibrium pressure
of the adsorbed material. Volumetric methods in use are described by
Harkins [l] and others [3] and [7].

- 10 -

NATURE OF PHYSICAL ADSORPTION

When a molecule of a liquid or vapor is attracted to the surface
of a solid, the result is that they are more or less loosely bound
together with the liberation of energy. While it is realized that the
forces involved are no different from other forces which bind liquids
and solids individually and cause deviations from ideal gas behavior,
they will be treated as a summation of distinct forces to better correl-
ate the theoretical approach with experimental data. Furthermore, it
should be realized that little is known of the real nature of the surface
itself and of the repulsive forces which oppose the attractive forces
at short distances. In addition, little is known of the equilibrium
distance between the surface and the molecules [2, 16] .

The Surface

It cannot be assumed that the surface of a crystalline adsorbent
is a smooth two-dimensional network of atoms or ions with the same geom-
etrical arrangement found inside the crystal. The surface ions are not
symmetrically surrounded and it is generally believed from theoretical
considerations that the positive ions would be found slightly inside the
crystal leaving a surface of negative ions displaced outward. Since pow-
dered solids have been used for experimental work, other disturbances
of the surface result in "active spots". Among these disturbances are
impurities which collect at the surfaces or at grain boundaries, remnants

- 11 -

of crystal faces, edges and corners, ridges, crevices, cavities, etc.

Protrusions provide the solid atoms or ions with less neighbors
and they are freer to enter into a chemical bond with an adsorbed
molecule. Physical adsorption, however, is not concerned with the
formation of chemical bonds. Consequently, the "active spots" for
physical adsorption are the crevices, cavities, insides of cracks, and
capillaries where an adsorbed molecule can get into contact with more
atoms of the adsorbent. Impurities, too, are important. An ionic
impurity could markedly increase the heat of adsorption if polar adsor-
bates are used. The first molecules to be adsorbed on the surface will,
therefore, often show a high adsorption energy.

Repulsive Forces

Whatever the nature of attraction forces between molecules or atoms
may be, they are checked by repulsion forces. The repulsion forces
arise from the impenetrability of the electron clouds and they balance
the attractive forces when the atoms are at equilibrium distance.

The expression,

E = — , (29)

rep n '

is usually used to represent the repulsion forces where b and n are
constants, and r is the distance between atoms. n varies from 9 for
hydrogen to 100 for carbon dioxide, and seems to be dependent upon the
number of electrons in both adsorbent and adsorbate .

- 12

Attractive Forces

These forces commonly called van der Waals ' forces include all
those which require no exchange or sharing of electrons . Ifonpolar and
polar van der Waal3* forces are usually considered separately to des-
cribe the adsorption of nonpolar and polar molecules, respectively.

Nonpolar forces result from the polarization of one of the mole-
cules participating in adsorption by the other molecule, atom, or
surface. The general expression for the van der Waals' energy of
interaction between two unlike atoms has been developed:
N I, Ip

where N is the number of atoms per cm in the surface, a and ao
are polarizabilities of the adsorbate and adsorbent, I and I are
the corresponding ionization energies, and r is the distance from
the adsorbed molecules to the surface . This energy is used to explain
the adsorption of hydrocarbons on ionic surfaces and polar molecules on
hydrophobic surfaces .

If the adsorbed molecule has a permanent dipole it is attracted
strongly to the surface of ionic crystals . The forces involved are
called polar van der Waals' forces, and when the dipole is situated
such that it may come into close proximity to the surface, significantly
high contributions to the adsorption energy is experienced. If the
positive end of the dipole is close to the end of a molecule, the mole-
cule will take an oriented position perpendicular to the surface . This

- 13 -

type of bonding is often called "hydrogen bonding" when hydrogen is
the positive atom concerned and negative ions form the outer layer of
the surface .

When the electrostatic field of the surface is denoted by F and
the polar molecule has a dipole moment, u , the energy contribution
is given by

E u = - F u . (31)

When the polar molecules have dipoles of nonperipheral character,
limited orientation will take place and nonpolar van der Waals ' forces
are dominant .

Occasionally the polarization of the adsorbed molecule will also
make a contribution to the adsorption energy. This contribution is
usually small but has been found to be described by the equation

E a = - Fa2/2 (32)

where F is the electrostatic field of the surface and a is the
polarizability of the adsorbed molecules . The energy contributions
of electrostatic polarization of the adsorbed molecules are far more
important on "active spots", and on projections or points of lattice
disturbances may exceed the contributions of nonpolar van der Waals'
forces .

Any adsorption phenomenon is a result of the cooperation of at
least one of the attraction forces and repulsion forces . The nonpolar
van der Walls* forces are always present and other forces may add

- 11+ -

significant contributions. Such forces are considered additive and the
mutual interaction between adjacent adsorbed molecules is considered
separately. The contribution due to interaction between adsorbed mole-
cules may also be significant in some cases; particularly after monolayer
coverage would such interaction come into play.

- 15 -

LITERATURE DATA

The current literature was searched for adsorption isotherms of
vapors adsorbed on hydrophilic solids. These isotherms were used to
evaluate the decrease in free energy by an integration of equations (28)
Graphical integration was employed from zero to saturation pressure.
The values determined are presented in the Appendix, Table I, and are
designated rt . The decrease in free energy at monolayer coverage is
presented in the Appendix, Table II. While the pressure at which mono-
layer films form is different for different systems it is fairly well
established that a relative pressure of 0.1 is a reasonable value for
monolayer coverage. The values calculated at a relative pressure of
0.1 are designated « . Free energy decreases for several vapors ad-
sorbed on mercury are presented in the Appendix, Table III. These
values were obtained from surface tension measurements [6] . Selected
heats of wetting are presented for comparison in the Appendix, Table IV.

It may be seen from equation (28),

Po2
*e = H Jo V d(ln P2)

that accurate values of « require accurate values for the volume

e

Relative pressure is the ratio of actual pressure, p , to the
saturation pressure, p .

- 16 -

adsorbed at low pressures. The lack of such low pressure data consti'
tutes a serious source of error in the calculations presented here .
Another source of error occurs at hi^h pressures where the equation
must be extrapolated to saturation pressure. Some analytical expres-
sions have been devised [l], but these were found unsatisfactory.

- IT

RESULTS AND CONCLUSIONS

Before any discussion of the data is attempted, it is desirable
to consider the quantities calculated. The conventional symbols estab-
lished by Harkins [l] and used in the section of this report describing
heats of emersion will also be used in this section. The reduction in
surface energy of a solid when it is emersed from a liquid is given as
y„ - 7 , where 7 is the surface free energy of the clean solid
and 7 is the free energy of the solid-liquid interface before emer-
sion. The corresponding Gibbs free energy term is given as y - y ,

if consistent symbols are employed, where 7 is the surface free

ox e

energy of the solid-vapor interface in equilibrium with the saturated

vapor. If 7 is the surface free energy of the bulk liquid, 7

Li ox e

is then equal to 7OT + 7 . It can be seen that the heats of wetting

oJu L

contain a term involving the free surface energy of the bulk liquid as
well as an entropy term. In other words, f , the free energy of
emersion is equal numerically to « , the free energy of adsorption,
plus 7 , the free energy of the liquid surface .

Lt

Consequently, the heat of wetting, 3i_/ qy \ , can be given as
VSL) = 7S - 7SL " T (oT" — \>z (4)

or

o7_ by

VSL) = *e + 7L ' T (oT~ ~^rhfL '

(29)

- 18 -

: -

ata
: : >py f or the are

I - 1 are * , %

z~zLe\

. . - ..
rtablisbe

. : _7_:er- _

: ere. ._ 7

ill cas a

a _

; a. _ . - -

; . - _ . :_

::" ■ : __• _: . : . e: _. _ . _ .rr_i

Sa-ur&ll^ . . . ■ _. - z^. : : -

lr^.-_- free ener 3

_r. free ene. r^s,

- -I ~c siz _= . . - - - _

is I: 7 I : tab] - . I -*=.;

Leant that _ ■

- - -

TABLE I

Comparison o

f Free Energy Terras with

Heat of Wett

in j Values

(ergs

i/cm )

WATER

ALCOHOL
n -propyl

n -butyl

n
e

it

h

*e "

hE

BaSO^

2Kb

66

kgo

77 50

360

Sn02

220

102

680

80 75

500

Ti02

190

30

520

103 Gj

350

monolayer coverage rather than at saturation. Sufficient data are not
available to determine if this trend is general, and poor data may be
the reason for such trend as is detected.

In considering specific items of data, one may notice the values
obtained when n -heptane is adsorbed by a metal and by a metal oxide.
The attractive forces involved are considered to be largely nonpolar
van der Waals ' forces described by equation (30) .

TABLE

II

Free Energy Value

s for

n -heptane

Adsorbed

on

Various Surfaces

(ergs /cm )

it

*e

Atomic Number

Atomic Radius

Fe (reduced)

23

53

26

1.165 A

Cu

2

29

29

1.173

A '<

Ag

9

37

^7

1.339

Sn

1

50

50

1.1*12

Pb

15

1*9

82

1.533

Sn09

17

5^

—

—

- 20 -

It may be observed that although no simple relationship exists, values
generally increase with increasing atomic number and radii. If it is
assumed that the polar izabili ties and ionization energies of the metals
are of the same order of magnitude, the forces would vary inversely as
the cube of the distance separating the adsorbed molecule and the surface.
From equation (29) it is seen the repulsi/e forces vary inversely as the
distance raised to some power no less than nine. The repulsive forces
should decrease more rapidly than the attractive forces as distance in-
creases . Such would appear to be the case if an increased atomic radius
of the adsorbent means that the adsorbate distance is increased; this
is not unreasonable. The values for iron may be incorrect; it was shown
[18] that iron could not be easily reduced to pure metallic powder and
that some oxide was always present . The values for tin and tin oxide
stron0ly point up the effect of an oxide on the surface of a metal.
That the free energy values at saturation pressures for the adsorption
of n-heptane are not significantly different is attributed to the belief
that the adsorbed hydrocarbon molecules do not assume an oriented posi-
tion but lie flat and are limited numerically regardless of their initial
attractions. That the initial attractions are different is evidenced
by the differences in the n values for monolayer coverage.

It is to be noted that adsorption of water is characterized by
large values of « and « . The polar van der Waals ' force, E ,
from equation (32) may be considered to describe the major force involved,
but cannot be the only force .

- 21 -

TABLE III

Adsorption of Water and Alcohol
(ergs /cm )

water (\± = 1 .3U D) n -propyl alcohol (u = l.bh D)

e

Ti02 190 80

Si02 2kk 54

BaSO^ 2U6 66

Sn 168

SnOg 220 102

Fe203 20p 72

n

e

«

108

69

110

55

77

50

83

*5

117

68

122

68

The effect of the characteristics of the adsorbents themselves
are observed if we compare % and v. values for alcohol and water .
ji values for water are no more than U-0 percent greater than alcohol
values, but n values indicate an increase of at least 100 percent.
Since the second and subsequent layers or partial layers contribute
to * , the large increase for water may be indicative of more water
adsorbing at saturation pressure . That dipole moment is not. the
answer even for initial attractions is realized by a comparison of
dipole moments. (See Table IV on following page.)

The higher i\ and n values for ethyl alcohol compared to

propyl alcohol may be the result of a smaller, more associated molecule

is
However, the fact /that different values for the same systems (anatase)

precludes any rigid conclusion.

- 22 -

TABLE TV
Adsorption on Ferric Oxide

u (dipole moment)
2.12 D

e

n

Bujiyl Chloride

5*

27

Water

1.8U D

205

72

Ethyl Alcohol

1.70 D

130

61

n -Propyl Alcohol

1.61* d

122

68

On all surfaces considered, the loss in free enrgy for alcohol
adsorption is intermediate between that of water and that of a hydro-
carbon. The n and n values for alcohol adsorption appear to

e

differ less than similar values for water adsorption. The alcohol
molecules are polar with a hydrocarbon tail and should be oriented per-
pendicular to the surface with the polar groups toward the polar solids
and hydrocarbon tails directed outward. These tails exhibit little
attractive energy and adsorption above monolayer coverage is believed
to be small compared to water. In fact, Harkins [l] states that ad-
sorption of n -propyl alcohol on barium sulfate is monomolecular almost
to saturation.

The temperature dependency and effect of chain length for initial
attraction are shown by studies of mercury (Table III in Appendix) . The
adsorbent while metallic is actually liquid and is presumed to have a
smooth, regular surface. An increase in temperature decreases the free
energy evolved in adsorption, as expected. Increasing the hydrocarbon

- 23 -

chain length of alcohols adsorbed on mercury increases the « values

and further adsorption indicates that subsequent layers continue this

trend [)] . Saturation values are not available to compare with the

adsorption of alcohols by other materials .

In summary, it may be 3aid that * values at monolayer coverage

seem to be more indicative of the attractive forces between a surface

and a liquid rather than equilibrium n values. Evidently, too many

of the characteristics of the liquid enter into the * values. Also,

e

differences in heats of emersion more nearly correspond to differences

in * values rather than differences in » values.

e

- 24 -

APPENDIX

- 25 -

*
anatase

TABLE I

Values of Spreading Pressure, n ,
Calculated from Adsorption Data at 25*C

(*e = ergs/cm )

n -propyl
.Water n -heptane Alcohol . Reference

Cu

n

[171

Cu(reduced)

29

[17]

Ag

33

[17]

Ag(reduced)

37

[17J

Pb

51

[171

Pb(reduced)

k9

[17]

Fe

5k

102

[1*]

Fe (reduced)

53

73

[JA]

Ti02 - I

2lU

--

85

Benzene

56

[3]

T10 - VI

228

--

90

Benzene

38

[3]

SxO,

2^

39

110

[3]

BaSO,

2h6

38

77

[3]

Sn02

220

5U

117

[13]

Sn

168

50

83

[13]

*

Ti02

190

KG

103

n -Butane
hi

[12]

Fe2°3

205

Ethyl Alcohol
136

122

Butyl Chloride
5k

[18]

- 26

TABLE II

Values of Spreading Pressure, «, at Monolayer
Coverage from Adsorption Data at 25 °C

(« = ergs/era )

Water

n-

-heptane

n -propyl
Alcohol

Reference

Cu

2.5

[17]

Cu(reduced)

2.0

[-71

Ag

9

[17]

Ag(reduced)

Q

[17]

Pb

15

[17]

Pb( reduced)

15

[17]

Fe

23

56

[Ik]

Fe (reduced)

23

30

U*0

TiOp - I

Qk

--

49

[31

Ti02 - VI

39

--

52

[J]

sio2

54

lif

55

[31

BaSO^

66

10

50

[3]

Sn02

102

17

75

[13]

Sn

--

1

45

[13]

*
K02

80

15

69

[12]

Pe2°3

72

Ethj

'1 Alcohol
6l

68

Butyl Chloride
27

[13]

anatase

- 27 -

TABLE III

Values of Spreading Pressure, a,

at Monolayer Coverage for Mercury

(it = cal/g-mole adsorbate)

methyl n -propyl
Temperature Water n -heptane alcohol alcohol amylalcohol Reference

68V7 8817 7379 8W5 10^06 [9]

19]

25°C

^0°C

59U9

3434

l^J

3246

IO5O0
9730

TABLE TV

Selected Values of Energy of

Emersion j

h , at 25°C
-e' - —

(h =
N e

er^s/cm )

Water

Ethyl
Acetate

Benzene

Butyl
Alcohol

Carbon
Tetrachloride

Reference

BaSO^

490

370

140

360

220

[11]

TiO a

520

360

150

350

240

[11]

sio2

600

460

150

420

-

[11]

Sn02

680

530

220

500

320

[11]

Ti02 b

550*

-

n -heptane

410

n -Butyl
Chloride 502

[113

a - anatase

b - rutile

3p0 later

- 28 -

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2383 (19^2).

k. Jura, G., and Hill, T. L., J. Am. Chem. Soc, jK, 1593 (1952).

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58, 307 0-95*0.

6. Ban^ham, D. H., Trans . Faraday Soc . , 33, 805 (1937).

7. Hill, T. L., Emmet t, P. H., and Joyner, L. G., J. Am. Chem. Soc,
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(19^-8) .

9. Kemball, C, and R ideal, E. K., Proc . Royal Soc, I87A, 53 (19^6);
190A, 117 (19^7).

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57, 251 (1953).

lU. Loeser, E. H., Harkins, W. D., and Twiss, S. B., J . Phys . Chem . ,
57, 591 (1953).

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Chem., 58, 837 ( 195*0 .

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Can. J. Chem., 33, 251 (1955).

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18. Fraoli, A. V., Ph.D. Dissertation, Lehigh Univ., I956.

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BIOGRAPHY

Sigmund Abraham, Jr. was born ^ November, 1924 in
man t gome ry Alabama. Parents were the late Sigmund Abraham and
Myrtle Harris Abraham. Upon graduation from high school, he
enlisted in the U. S. Navy and after service in the Pacific
Theatre during World War II, he graduated from the U. S. Naval
Academy, Annapolis, Maryland in 19^7 • After varied dut;, ,
including participation in the Korean conflict, he graduated
from the U. S. Naval Postgraduate School, Monterey, California
in 1953> having completed a course in Ordnance Engineering.
At the present time Mr. Abraham is a Lieutenant in the U. S.
Navy, serving aboard the U.S.S. IOWA. He is married to the
former Jan Virginia Spieldoch of San Francisco, California,
and has one child.

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l^o 33152

A168 Abraham

An investigation of
some free energies of
adsorption.

A168 Abraham

An investigation of some frpp
energies of adsorption.